I had the same issue with the Clek seat. Actually, I bought the Clek seat because our original Peg Perrego seat didn't fit correctly because of the armests sitting too far back (and interfering with the side boosters).
However, I figured out the trick to installing it and now it installs easily -- even with a seat protector.
As you're pushing it into the LATCH attachments, you need to press down toward the back of the seat. If you do one LATCH at a time, it's pretty simple and doesn't take too much force.
I even managed to use our seat protector (although I did finally decide to customize it by trimming it down to Model X seat size (and made cut-outs for the seat belts)). Our seat protector is the Summer Infant Duo (available on Amazon).
Seat belt extenders are, unfortunately, a necessity with Tesla. For some reason, they don't know how to measure the distance between LATCH and the seat buckle. Exact same problem on Model S.
They did improve slightly though versus Model S. The 3rd row seats work fine with the Clek and don't require a seatbelt extender.